As an important elastic parameter, seismic acoustic impedance is usually obtained through poststack inversion. However, there are usually two problems that limit the quality of the inversion results. First, conventional inversion methods typically use regularization terms to enhance the stability of the inversion results, and effective regularization terms are particularly important for accurately inverting seismic impedance. Second, most inversion methods adopt a trace-by-trace inversion strategy, resulting in poor lateral continuity when connecting the inversion results of all traces into a 2-D profile, especially for processing noisy data. To address these two problems, we propose a structure-oriented minimum entropy stabilizer for acoustic impedance inversion that enhances the lateral continuity of the inversion results while restoring the blocky structures of the strata and improving the resolution of the inversion results. The stabilizer consists of a structure-oriented regularization (SOR) operator and the minimum entropy norm. The SOR operator is constructed using the local dip estimated from the seismic data by the plane-wave destruction (PWD) algorithm and constrains the inverted impedance along the structural trend, making it more consistent with geological features. The minimum entropy norm restores the blocky structures and enhances resolution by imposing sparse constraints on the temporal and spatial derivatives of the impedance. Based on synthetic and field seismic data, we compare the inversion results of the proposed method with those of conventional Tikhonov regularization and total variation (TV) regularization methods. The results show that the proposed method exhibits superior performance, especially in processing noisy data.

The establishment of initial subsurface model is a crucial step for seismic inversion. An accurate and reasonable initial model can mitigate the ill-posedness of seismic inversion and improve the quality of inversion result. A common method for building initial model is the well-log data interpolation. However, the traditional well-log interpolation method ignores the structural information of the subsurface, resulting in the constructed initial model lacking geological meaning. We propose a novel structurally constrained modeling method (SCMM) to obtain a geologically reasonable initial impedance model for poststack seismic inversion. Well-log interpolation can be represented as an inverse problem. SCMM constrains the inversion process by using a regularization operator that forces the well-log data to be extended to the entire seismic working area along the subsurface local structural direction. First, we calculate the seismic dip from the poststack seismic profile. Then, we design the structural operator based on the estimated seismic dip information to constrain the interpolation process. Under the framework of inversion, the interpolation objective function can be established by combining the structural operator with the well-log data misfit term, and it can be solved efficiently by the conjugate gradient algorithm. Synthetic and field data tests show that the initial model built by SCMM is more consistent with the geological rules than that built by traditional method, and the poststack impedance inversion using SCMM is better than that using traditional modeling method in terms of convergence property and accuracy of inversion result.

As an effective approach of reservoir prediction, poststack impedance inversion has been widely used in industry. However, like other inverse problems, poststack impedance inversion is a quintessential ill-conditioned problem. Conventional impedance inversion methods often use regularization techniques such as Tikhonov-type regularization to improve the stability of the inversion solution. Nevertheless, because this type of regularization method constrains the inversion process by applying isotropic smoothness to the impedance, it will result in blurred boundaries and micro-geological structures, thereby reducing the resolution of the inversion result. In order to address this problem, we have introduced a structure-oriented regularization (SOR) method based on the local geological structural direction for impedance inversion. Compared with conventional isotropic smooth constraints, SOR can apply smoothness along the direction of geological structures, so it can effectively protect significant geological information from being blurred. Three steps are required to complete the SOR-based seismic impedance inversion method. To begin with, the structural orientations are estimated from seismic image. Then, the SOR term is constructed and combined with the multitrace seismic data misfit term to formulate the objective function for the inversion of impedance. Finally, the objective function can be easily solved by the conjugate gradient (CG) method. We compare our method with the classic model-based impedance inversion method on synthetic and real seismic data. The inversion results demonstrate the benefit of our method in seismic impedance inversion.

Impedance inversion is an effective method to estimate the properties of subsurface model from poststack seismic data. However, owing to the low quality of seismic data and other reasons, impedance inversion methods usually suffer from spatial discontinuities and low resolution. In order to overcome these problems, we have developed an impedance inversion method based on geological structure-guided total variation (GSGTV) constraint. Different from traditional total variation (TV) constraint, GSGTV considers the spatial distribution of geological structures instead of imposing gradient constraints on impedance only in fixed directions (horizontal and vertical). Therefore, GSGTV not only retains the advantage of traditional TV that can preserve the edge of layer but also overcomes the shortcomings of traditional TV that is only suitable for inverting block structures. This ensures that GSGTV can simultaneously improve the resolution and spatial continuity of the inversion result. The realization of impedance inversion method based on GSGTV constraint requires three steps. First, estimate the local structural orientation of the subsurface from seismic data. Then, construct GSGTV regularization term based on the local structural orientation. Finally, establish the inversion objective function and solve the function by the split-Bregman iterative algorithm. We compared the proposed method and the impedance inversion method based on traditional TV constraint with synthetic and real seismic data. The inversion results confirm that our method can improve the resolution and spatial continuity.

Absorption in subsurface media severely degrades seismic data quality. Seismic attenuation compensation as an important processing method can effectively improve the resolution and fidelity of seismic data. Based on sparse reflectivity model and attenuated convolution function, inversion-based compensation approaches show better stability and accuracy over traditional direct compensation schemes. However, conventional inversion-based compensation methods are conducted on single trace, which ignore the subsurface spatial continuity and make the compensated result contaminated with high-frequency noise. In this paper, we develop a structurally constrained multichannel L1-2 minimization for seismic attenuation compensation. We first estimate structure tensors from migrated seismic images. The structure tensors can be decomposed by eigenvalues and eigenvectors, which can reflect the structural orientations. Then, we introduce the estimated orientations as a regularization term to the L1-2 inversion-based compensation objective function. In this way, we can improve the stability of the compensation result and enhance the spatial continuity of the compensated seismic reflectors. The structure-guided L1-2 regularized compensation objective function can be efficiently solved via difference of convex algorithm and alternating direction method of multipliers. Synthetic and field data examples demonstrate that the proposed method possesses superior performance over conventional L1-2 regularized inversion-based compensation.

Seismic deconvolution is an effective approach to improve the resolution of seismic data and plays an important role in migration imaging, reservoir prediction and other fields. However, conventional deconvolution methods are usually based on sparse-type regularization (e.g.,$L_{1}$-norm) and adopt a trace-by-trace inversion strategy to reconstruct the subsurface reflectivity series. Although such methods can improve the resolution of seismic records to a certain extent, the lack of spatial constraint will result in poor spatial continuity in the reconstructed reflectivity. This phenomenon is particularly obvious in regions with complicated geologic structures. For the purpose of overcoming this issue, we have developed a structure-oriented regularization-based multichannel sparse spike deconvolution (SOR-based MSSD) method. This method imposes$L_{1}$-norm regularization on the reflectivity to obtain the high-resolution subsurface reflectivity series and imposes structure-oriented regularization (SOR) on the expected high-resolution seismic data to improve the spatial continuity of the inversion result. First, we construct SOR term based on the local structural orientations which can be estimated from the poststack seismic data. Then, we integrate the seismic data misfit term, the$L_{1}$-norm constraint term, and the SOR term to formulate the objective function. At last, we use the alternating direction method of multipliers (ADMMs) to efficiently solve the objective function. We compare the SOR-based MSSD with existing methods by using synthetic and field data. Both deconvolution examples illustrate the performance of proposed method in terms of improving the spatial continuity.